1. SOURCES OF UNCERTAINTY
A. Repeatability (Type A)
B. Buffers (Type B)
C. Resolution of pH meter (Type B)
D. Linearity (Type B)
E. Temperature (Type B)
2.Quntification of Sources of Uncertainty
A. Repeatability (Type A)
 |
| Repeatability calculation (Type A Uncertainty) |
Formula / Expression of find the Repeatability (Standard uncertainty)
Mean = AVERAGE(B4:B13)
(X - Mean) = $B4-$C$4
=UUT Value - Mean
(X - Mean)^2 = ($D4)^2
=(UUT Value - Mean)^2
Standard Deviation = STDEV(B4:B13)
Repeatability (Standard Uncertainty) = F4/SQRT(10)
=Standard Deviation / square root (number of Sample)
B. Buffers:
Following Buffers are used in Calibration of pH Meter:
a) 4.01 with ± 0.02 uncertainty declared by manufacturer.
b)7.00 with ± 0.01 uncertainty declared by manufacturer.
c) 10.01 with ± 0.03 uncertainty declared by manufacturer.
Uncertainty contribution (unc) = SQRT(SUMSQ(D17:D19))
=√0.00502+0.00142+0.00302
=0.005992
Standard Uncertainty of buffers = pH measured * unc
=C4*D21
=0.005992*7.013
=0.0420
C. Resolution of pH meter (Type B)
Resolution of UUT (pH Meter) = 0.01
In uncertainty Contribution we take the half of the resolution
=0.01/2
=0.005
So the standard uncertainty is calculated using the assumption of a Rectangular Distribution.
=0.005/√3
=0.00289
Rectangular Probability Distribution
if the limits can be determined but there is no knowledge of behavior within the limit and the value of measurand is equally likely to lie anywhere within the limit, then the distribution of uncertainty is assumed as Rectangular Distribution.
Additional information is available about the Resolution .We take the Rectangular distribution.
D. Linearity (Type B)
Accuracy or Permissible or Linearity of UUT is ±0.10%
=0.10/√3
=0.057
Standard uncertainty is calculated using the assumption of a Rectangular Distribution.
E. Temperature (Type B)
The pH has inbuilt temperature compensation factor is available ,pH value is not more affected by the temperature, so we can neglect this Type B uncertainty part.
3. Combined Standard Uncertainty =
Combined Uncertainty =Uc=√0.01542 + 0.00602 + 0.00292 + 0.05772
=0.073
4.Expanded Uncertainty (at 95% CL)
CL = Confidence Level
k=2
U=k*uc
=2*0.073
=0.146
Reporting the Expanded uncertainty in the certificate is like that
pH = 7.01 ± 0.15
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